Portfolio risk refers to a wide range of threats to the financial well-being of an investment portfolio. Accordingly, the field of portfolio risk management includes diverse functions such as portfolio optimization and capital allocation, and it relies on a broad and complex set of quantitative measures. One of the most important of these is volatility, which is the standard deviation of loss or return of the portfolio. Volatility plays a significant role in every aspect of risk management. However, it is well known that volatility does not give a complete picture of financial risk. For example, it does not properly describe the extreme events that are prevalent in financial markets and it provides no insight into the temporal aspects of risk.
Volatility forecasts are often supplemented with estimates of value-at-risk (VaR), which is the pth quantile of the loss distribution for a specified confidence level p. Since the value of p can be varied, VaR measures risk that is not included in volatility estimates. However, neither VaR nor volatility forecasts the risk of severe loss, which is difficult to measure precisely due to intrinsic data constraints. A crude estimator of severe loss is expected shortfall (ES), which is the average excess loss given that the VaR limit is breached.
In principle, volatility, value-at-risk, expected shortfall, and all other quantitative measures of portfolio risk can be derived from the loss surface, which is the set of portfolio loss distributions at a number of time horizons. Thus, the loss surface has the conceptual virtue of providing a common perspective on different facets of portfolio risk. However, there are many practical difficulties involved in its estimation.